{
  "id": "1604.05262",
  "version": "v1",
  "published": "2016-04-18T17:40:52.000Z",
  "updated": "2016-04-18T17:40:52.000Z",
  "title": "A note on the double-critical graph conjecture",
  "authors": [
    "Hao Huang",
    "Alexander Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A connected $n$-chromatic graph $G$ is double-critical if for all the edges $xy$ of $G$, the graph $G-x-y$ is $(n-2)$-chromatic. In 1966, Erd\\H os and Lov\\'asz conjectured that the only double-critical $n$-chromatic graph is $K_n$. This conjecture remains unresolved for $n \\ge 6.$ In this short note, we verify this conjecture for claw-free graphs $G$ of chromatic number $6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-18T17:40:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "double-critical graph conjecture",
      "chromatic graph",
      "conjecture remains",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160405262H"
    }
  }
}